Adding holes to this sphere
Steps:

First of all activate LoopTools add-on in User Preferences, than:


CTRL+Shift+B to Bevel vertices.
MouseWheel to add more cuts or press F6 to see menu with Bevel options.
W > LoopTools > Circle.
CTRL+Num -  to select less.
X > Delete Vertices.




Edit:

For OP model holes will have different number of vertices. But besides that everything is working just fine.



As a workaround you can first select vertices with 3 connected edges and make for example 5 Bevel cuts: 3 edges x 5 cuts = 15 vertices.

Than do the same thing with vertices with 5 edges connected with 3 cuts: 5 edges x 3 cuts = 15 vertices.